BSGS requires a public key (e.g. puzzles 135, 140, 145, 150, 155, 160, or a signed message or TX for all other puzzles).

IDK what you're doing but BSGS is fully deterministic, unless you run multiple smaller BSGS over (random) subintervals, or you tradeoff the 100% chances to find the key with a smaller memory footprint (potentially missing the solution). But before all, you should answer yourself why you want to use BSGS in the first place. For 135 there might not be enough storage on our planet to even finish off iterating through the baby steps, let alone enough fast RAM to store all of that, to run through the giant steps. At each giant step, a lookup must be performed in the table, but if you can't have the table (or it is not a fast table, which means that all and any of it needs to be directly accessible instantly, not using any network, cloud, cables, compression, etc.) you're at a dead end.